Labelings A and B are modified from [1]}.
By euclid one only needs to consider those double spiders in 2 types resulting in simplified proofs with less cases considered than in [1]}. Moreover, if the order of the path \(X\)  is not revised for the special case (\(*\) ) in Labeling B as in [1]},
direct calculation shows that \(\phi (u)=\phi (v)\)  when \(\alpha =1\) ; not treating this subtlety caused an error to occur in [1]}. For instance, in [10]10 (b), reversing the middle path \(X\)  gives \(\phi (u)=\phi (v)= 32\) .
